The EM/MPM algorithm for segmentation of textured images: analysisand further experimental results

In this paper we present new results relative to the "expectation-maximization/maximization of the posterior marginals" (EM/MPM) algorithm for simultaneous parameter estimation and segmentation of textured images. The EM/MPM algorithm uses a Markov random field model for the pixel class labels and alternately approximates the MPM estimate of the pixel class labels and estimates parameters of the observed image model. The goal of the EM/MPM algorithm is to minimize the expected value of the number of misclassified pixels. We present new theoretical results in this paper which show that the algorithm can be expected to achieve this goal, to the extent that the EM estimates of the model parameters are close to the true values of the model parameters. We also present new experimental results demonstrating the performance of the EM/MPM algorithm.     

结合EM/MPM算法和Voronoi划分的图像分割方法

为了实现在模型参数先验分布知识未知情况下进行基于区域和统计方法的图像分割,同时获取更精确的模型参数估计结果,提出了一种结合Voronoi划分技术、最大期望值(Expectation Maximization, EM)和最大边缘概率(Maximization of the Posterior Marginal, MPM)算法的图像分割方法。该方法利用Voronoi划分技术将图像域划分为若干子区域,待分割图像中的同质区域可以由一组子区域拟合而成,并假定同一同质区域内像素强度服从同一独立的正态分布,从而建立图像模型,然后结合EM/MPM算法进行图像分割和模型参数估计,其中,MPM算法用于实现面向同质区域的图像分割,EM算法用于估计图像模型参数。为了验证本文图像分割方法,分别对合成图像和真实图像进行了分割实验,测试结果的定性和定量分析表明了该方法的有效性和准确性。      

Hierarchical stochastic image grammars for classification and segmentation.

We develop a new class of hierarchical stochastic image models called spatial random trees (SRTs) which admit polynomial-complexity exact inference algorithms. Our framework of multitree dictionaries is the starting point for this construction. SRTs are stochastic hidden tree models whose leaves are associated with image data. The states at the tree nodes are random variables, and, in addition, the structure of the tree is random and is generated by a probabilistic grammar. We describe an efficient recursive algorithm for obtaining the maximum a posteriori estimate of both the tree structure and the tree states given an image. We also develop an efficient procedure for performing one iteration of the expectation-maximization algorithm and use it to estimate the model parameters from a set of training images. We address other inference problems arising in applications such as maximization of posterior marginals and hypothesis testing. Our models and algorithms are illustrated through several image classification and segmentation experiments, ranging from the segmentation of synthetic images to the classification of natural photographs and the segmentation of scanned documents. In each case, we show that our method substantially improves accuracy over a variety of existing methods.     

Multiresolution Gauss-Markov random field models for texturesegmentation

This paper presents multiresolution models for Gauss-Markov random fields (GMRFs) with applications to texture segmentation. Coarser resolution sample fields are obtained by subsampling the sample field at fine resolution. Although the Markov property is lost under such resolution transformation, coarse resolution non-Markov random fields can be effectively approximated by Markov fields. We present two techniques to estimate the GMRF parameters at coarser resolutions from the fine resolution parameters, one by minimizing the Kullback-Leibler distance and another based on local conditional distribution invariance. We also allude to the fact that different GMRF parameters at the fine resolution can result in the same probability measure after subsampling and present the results for first- and second-order cases. We apply this multiresolution model to texture segmentation. Different texture regions in an image are modeled by GMRFs and the associated parameters are assumed to be known. Parameters at lower resolutions are estimated from the fine resolution parameters. The coarsest resolution data is first segmented and the segmentation results are propagated upward to the finer resolution. We use the iterated conditional mode (ICM) minimization at all resolutions. Our experiments with synthetic, Brodatz texture, and real satellite images show that the multiresolution technique results in a better segmentation and requires lesser computation than the single resolution algorithm.     

EM image segmentation algorithm based on an inhomogeneous hidden MRF model

This paper introduces a Bayesian image segmentation algorithm that considers the label scale variability of images. An inhomogeneous hidden Markov random field is adopted in this algorithm to model the label scale variability as prior probabilities. An EM algorithm is developed to estimate parameters of the prior probabilities and likelihood probabilities. The image segmentation is established by using a MAP estimator. Different images are tested to verify the algorithm and comparisons with other segmentation algorithms are carried out. The segmentation results show the proposed algorithm has better performance than others.     

Weighted maximum posterior marginals for random fields using an ensemble of conditional densities from multiple Markov chain Monte Carlo simulations

The ability of classification systems to adjust their performance (sensitivity/specificity) is essential for tasks in which certain errors are more significant than others. For example, mislabeling cancerous lesions as benign is typically more detrimental than mislabeling benign lesions as cancerous. Unfortunately, methods for modifying the performance of Markov random field (MRF) based classifiers are noticeably absent from the literature, and thus most such systems restrict their performance to a single, static operating point (a paired sensitivity/specificity). To address this deficiency we present weighted maximum posterior marginals (WMPM) estimation, an extension of maximum posterior marginals (MPM) estimation. Whereas the MPM cost function penalizes each error equally, the WMPM cost function allows misclassifications associated with certain classes to be weighted more heavily than others. This creates a preference for specific classes, and consequently a means for adjusting classifier performance. Realizing WMPM estimation (like MPM estimation) requires estimates of the posterior marginal distributions. The most prevalent means for estimating these--proposed by Marroquin--utilizes a Markov chain Monte Carlo (MCMC) method. Though Marroquin's method (M-MCMC) yields estimates that are sufficiently accurate for MPM estimation, they are inadequate for WMPM. To more accurately estimate the posterior marginals we present an equally simple, but more effective extension of the MCMC method (E-MCMC). Assuming an identical number of iterations, E-MCMC as compared to M-MCMC yields estimates with higher fidelity, thereby 1) allowing a far greater number and diversity of operating points and 2) improving overall classifier performance. To illustrate the utility of WMPM and compare the efficacies of M-MCMC and E-MCMC, we integrate them into our MRF-based classification system for detecting cancerous glands in (whole-mount or quarter) histological sections of the prostate.     

基于B样条的小波分解快速算法

在对一类广义多分辨模型研究基础上，以样条函数空间为例，全面剖析了基于Ｂ样条函数的多分辨塔式结构与算法，并详细给出了各滤波器参数。对一维信号与二维图象的仿真研究表明该算法简洁、快速，具有推广应用价值。     

Image segmentation using hidden Markov Gauss mixture models.

Image segmentation is an important tool in image processing and can serve as an efficient front end to sophisticated algorithms and thereby simplify subsequent processing. We develop a multiclass image segmentation method using hidden Markov Gauss mixture models (HMGMMs) and provide examples of segmentation of aerial images and textures. HMGMMs incorporate supervised learning, fitting the observation probability distribution given each class by a Gauss mixture estimated using vector quantization with a minimum discrimination information (MDI) distortion. We formulate the image segmentation problem using a maximum a posteriori criteria and find the hidden states that maximize the posterior density given the observation. We estimate both the hidden Markov parameter and hidden states using a stochastic expectation-maximization algorithm. Our results demonstrate that HMGMM provides better classification in terms of Bayes risk and spatial homogeneity of the classified objects than do several popular methods, including classification and regression trees, learning vector quantization, causal hidden Markov models (HMMs), and multiresolution HMMs. The computational load of HMGMM is similar to that of the causal HMM.     

Adaptive scale fixing for multiscale texture segmentation.

This paper addresses two challenging issues in unsupervised multiscale texture segmentation: determining adequate spatial and feature resolutions for different regions of the image, and utilizing information across different scales/resolutions. The center of a homogeneous texture is analyzed using coarse spatial resolution, and its border is detected using fine spatial resolution so as to locate the boundary accurately. The extraction of texture features is achieved via a multiresolution pyramid. The feature values are integrated across scales/resolutions adaptively. The number of textures is determined automatically using the variance ratio criterion. Experimental results on synthetic and real images demonstrate the improvement in performance of the proposed multiscale scheme over single scale approaches.     

Adaptive parametric estimation and classification of remotelysensed imagery using a pyramid structure

An unsupervised region-based image segmentation algorithm implemented with a pyramid structure has been developed. Rather than depending on traditional local splitting and merging of regions with a similarity test of region statistics, the algorithm identifies the homogeneous and boundary regions at each level of the pyramid; the global parameters of each class are then estimated and updated with the values of the homogeneous regions represented at that level of the pyramid using mixture distribution estimation. The image is then classified through the pyramid structure. Classification results obtained for both simulated and SPOT imagery are presented     

Motion estimation using a complex-valued wavelet transform

This paper describes a new motion estimation algorithm that is potentially useful for both computer vision and video compression applications. It is hierarchical in structure, using a separable two-dimensional (2-D) discrete wavelet transform (DWT) on each frame to efficiently construct a multiresolution pyramid of subimages. The DWT is based on a complex-valued pair of four-tap FIR filters with Gabor-like characteristics. The resulting complex DWT (CDWT) effectively implements an analysis by an ensemble of Gabor-like filters with a variety of orientations and scales. The phase difference between the subband coefficients of each frame at a given subpel bears a predictable relation to a local translation in the region of the reference frame subtended by that subpel. That relation is used to estimate the displacement field at the coarsest scale of the multiresolution pyramid. Each estimate is accompanied by a directional confidence measure in the form of the parameters of a quadratic matching surface. The initial estimate field is progressively refined by a coarse-to fine strategy in which finer scale information is appropriately incorporated at each stage. The accuracy, efficiency, and robustness of the new algorithm are demonstrated in comparison testing against hierarchical implementations of intensity gradient-based and fractional-precision block matching motion estimators     

融合对称特性的混合标签传递半监督直觉模糊聚类图像分割

现有的直觉模糊聚类算法应用于图像分割时,往往只考虑图像的像素信息,忽略了图像的几何特征和区域信息,使得分割效果不太理想。为了提高直觉模糊聚类算法的分割性能,提出一种融合对称特性的混合标签传递半监督直觉模糊聚类算法。该算法首先对图像进行对称轴检测获取图像的对称特性,接着利用图像的对称特性进行对称像素的标签传递并改进像素对聚类中心的直觉模糊距离测度,然后设计一种混合标签传递半监督策略,对所有像素进行隶属度的估计并将其作为监督隶属度进行引入,随后构建融合对称特性的混合标签传递半监督直觉模糊聚类目标函数,通过聚类获得最终的分割结果。两个彩色图像库上的实验结果表明,该算法能够将目标从复杂背景中完整的分割出来,分割性能优于对比算法。      

Fuzzy random fields and unsupervised image segmentation

Statistical unsupervised image segmentation using fuzzy random fields is treated. A fuzzy model containing a hard component, which describes pure pixels, and a fuzzy component which describes mixed pixels, is introduced. A procedure for simulating, a fuzzy field based on a Gibbs sampler step followed by a second step involving white or correlated Gaussian noises is given. Then the different steps of unsupervised image segmentation are studied. Four different blind segmentation methods are performed: the conditional expectation, two variants of the maximum likelihood, and the least squares approach. The parameters required are estimated by the stochastic estimation maximization (SEM) algorithm, a stochastic variant of the expectation maximization (EM) algorithm. These fuzzy segmentation methods are compared with a classical hard segmentation method, without taking the fuzzy class into account. The study shows that the fuzzy SEM algorithm provides reliables estimators. Furthermore, fuzzy segmentation always improves upon the hard segmentation results     

深度图像分割中的面元优化描述

该文提出了一种新的参数化面元的优化描述方法,基于二次型面表示模型,物体表面参数由深度图像数据拟合得到,基于一种改进的纠偏曲面拟合方法,提出了一个正态分布概率模型来描述面元估计的统计性质,并显式定义了面元描述的可靠性度量,以面元提取为目的,提出了一种新的基于参数估计的深度图像分割方法,在建立区域一致性判别优化准则的同时,使得区域增长总是收敛于所提取面元的最可靠描述,文中给出了实际深度图像分割的实验结果。     

A spatially constrained generative asymmetric Gaussian mixture model for image segmentation

Accurate image segmentation is an essential step in image processing, where Gaussian mixture models with spatial constraint play an important role. Nevertheless, most methods suffer from one or more challenges such as limited robustness to noise, over-smoothness for segmentations, and lack of flexibility to fit the observed data. To address these issues, in this paper, we propose a generative asymmetric Gaussian mixture model with spatial constraint for image segmentation. The asymmetric distribution is modified to be easily incorporated the spatial information. Then our asymmetric model can be constructed based on the posterior and prior probabilities of within-cluster and between-cluster. Based on the Kullback-Leibler divergence, we introduce two pseudo-likelihood quantities which consider the neighboring priors of within-cluster and between-cluster. Finally, we derive an expectation maximization algorithm to maximize the approximation of the data log-likelihood. We compare our algorithm with state-of-the-art segmentation approaches to demonstrate the superior performance of the proposed algorithm.     

Gradient-based multiresolution image fusion

A novel approach to multiresolution signal-level image fusion is presented for accurately transferring visual information from any number of input image signals, into a single fused image without loss of information or the introduction of distortion. The proposed system uses a "fuse-then-decompose" technique realized through a novel, fusion/decomposition system architecture. In particular, information fusion is performed on a multiresolution gradient map representation domain of image signal information. At each resolution, input images are represented as gradient maps and combined to produce new, fused gradient maps. Fused gradient map signals are processed, using gradient filters derived from high-pass quadrature mirror filters to yield a fused multiresolution pyramid representation. The fused output image is obtained by applying, on the fused pyramid, a reconstruction process that is analogous to that of conventional discrete wavelet transform. This new gradient fusion significantly reduces the amount of distortion artefacts and the loss of contrast information usually observed in fused images obtained from conventional multiresolution fusion schemes. This is because fusion in the gradient map domain significantly improves the reliability of the feature selection and information fusion processes. Fusion performance is evaluated through informal visual inspection and subjective psychometric preference tests, as well as objective fusion performance measurements. Results clearly demonstrate the superiority of this new approach when compared to conventional fusion systems.     

A segmentation-based predictive multiresolution image coder

Recursive rectilinear tessellations like quadtree are widely used in image coding, but a regular tessellation, despite simple geometry, may not suit image compression because it is too rigid to reflect the scene structure of an image. The paper presents a new image pyramid formed by adaptive, tree-structured segmentation to be a framework of a predictive multiresolution image coder. Subjectively appealing compression results are obtained at different resolutions by scene-adaptive, tree-structured segmentation and by exploiting the statistical dependency between the layers of the image pyramid. The adaptive segmentation-based image coder is constructed by recursive, least-squares piecewise functional approximation. The seemingly expensive encoding process can be made efficient by an incremental least-squares computation technique. The decoding is simple and can be done in real time if assisted by existing hardware technology.     

基于不完全分层MRF的非监督图象分割

分层马尔可夫随机场(MRF)图象模型由于层间具有因果关系,且这种因果关系符合图象的性质,使基于该模型的图象处理时间比平面MRF模型所用的时间大为减少.针对作者提出的一种新的分层马尔可夫图象模型——不完全分层模型,导出EM算法以估计模型参数.算法继承了分层模型非迭代算法运算速度快的优点,并因为模型结构的简化进一步减少了计算量,算法在模型的最上层加入了平面节点间信息的交互,以较少的计算换来了更加精确的参数估计结果.算法用于图象非监督分割的实验表明,和分层模型算法相比,其处理速度更快、由所估计的参数得到了更好或相当的分割结果,尤其适合大幅面图象的处理.     

Multiresolution Vector Quantization for Video Coding

In this work, we propose a coding technique that is based on the generalized block prediction of the multiresolution subband decomposition of motion compensated difference image frames. A segmentation mask is used to distinguish between the regions where motion compensation was effective and those regions where the motion model did not succeed. The difference image is decomposed into a multiresolution pyramid of subbands where the highest resolution subbands are divided into two regions, based on the information given by the segmentation mask. Only the coefficients of the regions corresponding to the motion model failure are considered in the highest resolution subbands. The remaining coefficients are coded using a multiresolution vector quantization scheme that exploits inter-band non-linear redundancy. In particular, blocks in one subimage are predicted from blocks of the adjacent lower resolution subimage with the same orientation. This set of blocks plays the role of a codebook built from coefficients inside the subband decomposition itself. Whenever the inter-band prediction does not give satisfactory results with respect to a target quality, the block coefficients are quantized using a lattice vector quantizer for a Laplacian source.